Mesh analysis worksheet with answers

Free printable Mesh analysis worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
R1​ = 6 ΩR2​ = 4 Ω+−V1​8 VR3​2 ΩAR4​10 ΩBI1​I2​

Use mesh analysis to find the mesh current I1 (clockwise).

V1 = 8 VR1 = 6 ΩR2 = 4 ΩR3 = 2 ΩR4 = 10 Ω
I1 = A
2.Easy
R1​ = 12 Ω+−VR1​R2​ = 3 Ω+−V1​15 VR3​12 ΩAR4​10 ΩBI1​I2​

Use mesh analysis to find the voltage VR1 across R1 with the polarity shown.

V1 = 15 VR1 = 12 ΩR2 = 3 ΩR3 = 12 ΩR4 = 10 Ω
VR1 = V
3.Medium
R1​ = 2 ΩR2​ = 6 Ω+−V1​9 VR3​2 ΩA+−V2​12 VI1​I2​

Use mesh analysis to find the mesh current I2 (clockwise).

V1 = 9 VV2 = 12 VR1 = 2 ΩR2 = 6 ΩR3 = 2 Ω
I2 = A
4.Medium
R1​ = 2 ΩR2​ = 2 Ω+−V1​12 VR3​6 Ω+−VR3​A+−V2​24 VI1​I2​

Use mesh analysis to find the voltage VR3 across R3 with the polarity shown.

V1 = 12 VV2 = 24 VR1 = 2 ΩR2 = 2 ΩR3 = 6 Ω
VR3 = V
5.Hard
R1​ = 3 ΩR2​ = 2 ΩIR2​R3​ = 8 Ω+−V1​5 VR4​6 ΩAR5​6 ΩB+−V2​15 VI1​I2​I3​

Use mesh analysis to find the current IR2 through R2 in the direction of the arrow.

V1 = 5 VV2 = 15 VR1 = 3 ΩR2 = 2 ΩR3 = 8 ΩR4 = 6 ΩR5 = 6 Ω
IR2 = A
6.Hard
R1​ = 10 ΩR2​ = 15 ΩR3​ = 5 Ω+−V1​18 VR4​15 ΩAR5​20 ΩIR5​B+−V2​6 VI1​I2​I3​

Use mesh analysis to find the current IR5 through R5 in the direction of the arrow.

V1 = 18 VV2 = 6 VR1 = 10 ΩR2 = 15 ΩR3 = 5 ΩR4 = 15 ΩR5 = 20 Ω
IR5 = A

Answer key

  1. 1. I1 = 1.032 A
  2. 2. VR1 = 9.868 V
  3. 3. I2 = −1.071 A
  4. 4. VR3 = 15.43 V
  5. 5. IR2 = −0.4167 A
  6. 6. IR5 = 0.288 A

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